ME 440 - 09 CNC System (Rev. 3)

O tli CNC S tOutline – CNC System• CNC System

– Direct ControlDirect Control– Indirect Control

• Architecture of CNC• Architecture of CNC System – Control AlgorithmControl Algorithm

• InterpolatorLinear– Linear

– Circular

Chapter 9 ME 440 2

Computer Numerical ControlComputer Numerical Control• CNC is a multi-processor control system designed

to perform the tasks commonly encountoured into perform the tasks commonly encountoured in metal working machinery and other machine tools:

– Motion control / Servo control• Multi-axis motion control• Spindle motion control

– Peripheral unit control / PLC• Tool changer / turret• Coolant / lubricant control• Tool alignment / other auxillary functions

Command generation– Command generation• Interpolation / command shaping• Machine tool cycles• Tool ofset compensation• Passive error compensation

– Diagnostics and calibration– User Interfacing

• Program editing / storage / simulation• File management• Tool management• Tool management• Manual data input (MDI) • Machine / human interfacing

Courtesy of Heidenhain Corp.

Chapter 10 ME 440 3

CNC Systemsy

CNC SystemNC

Indirect Control System

Torq

ueco

mm

and

CNC System

i Ser oPosi

tion

com

man

d

M t

NCProgram

feedstoollocation

P i i

PartTable

Interpolator

cMotionController

Servomotor

Angular position feedback

c MotorDrive

Positionsensor

Ball Screw Shaft Nut

CNC S tNC

Direct Control System

Torq

ueom

man

d

CNC System

SPosi

tion

omm

and

M

NCProgram

feedstoollocation

Positionsensor

PartTable

Interpolator

cMotionController

Servomotor

Direct position feedback

P c MotorDrive Ball Screw Shaft Nut

Chapter 10 ME 440 4

Generic CNC SystemGeneric CNC SystemDrive +ut ac

e

CuttingForces

Controle(k) m(k) x(t)x*(k) + m(t) τm(t)Interpolator

Torquecommand(voltage)Po

sitio

nco

mm

and

Drive +Motor Feed Drive

Out

puIn

terf

aControlAlgorithm

e(k) ( )( )

_

( )

Clock

m

T

Motortorque

NCProgram

Sens

ornt

erfa

ce PositionSensor

x(k)

Clock

Carriage's position

SynchronizationSignal

CNC System

S In

• In this direct control system, the position of the carriage y , p g(x) is measured and sampled by this simplified CNC system. The interpolator comp tes the desired position ( *) of the• The interpolator computes the desired position (x*) of the carriage at a particular instant in time using the NC program.

Chapter 10 ME 440 5

p g

Generic Control System (Cont’d)Generic Control System (Cont d)• The control algorithm first determines the deviationThe control algorithm first determines the deviation

(e = x*-x) of the feed-drive system from the desired path and then calculates the corrective action (m).

• The correction signal (called manipulation) is sent to the output interface generating a corresponding voltage m(t).

• This voltage serves as a torque command for the motor drive which in turns controls the servo-motor to produce th d i d tthe desired torque.

• Hence, the generated torque (τm) compensates the di t b th f d d i t d t thdisturbance on the feed-drive system and puts the carriage back to its desired course.

Chapter 10 ME 440 6

Computer Controlp

• Each physical quantity (such as position• Each physical quantity (such as position measurement, error, etc.) in CNC system (a.k.a. control computer) is represented by acontrol computer) is represented by a corresponding binary number with a finite length:

Byte / word– Byte / word– Integer, long integer

Floating point number etc– Floating point number etc.• All computations and I/O operations are

h i d b t l ksynchronized by a master clock.

Chapter 10 ME 440 7

Computer Control (Cont’d)p ( )

Inside the comp ter each q antit is alid• Inside the computer, each quantity is valid at only discrete-time intervals: – t = {0, T, 2T, 3T, ..., kT, ...}– T is called sampling period of the computer.T is called sampling period of the computer.

• In discrete-time domain, the time dependence among various quantities ofdependence among various quantities of interest are represented by a time index:

(t kT) (kT) (k) h k 0 1 2– x(t=kT) = x(kT) = x(k) where k = 0, 1, 2, ...– Integer k is called time index.

Chapter 10 ME 440 8

Control AlgorithmControl Algorithm• Control algorithm can be expressed in terms of a finite g p

difference equation. That is, it is an algebraic expression which depends on not only the history of the input but also that of the output:that of the output:

∑ ∑ −+−−=I J

ji jkebikmakm )()()( ∑ ∑= =i j

ji j1 0

)()()(

ai, bj are the constant coefficients of the equation;ai, bj are the constant coefficients of the equation;m(k) current value of the output (manipulation) @ t = kT;m(k-1) is old value of m @ t = (k-1)T, ... ;e(k) current value of the input (error) @ t = kT;e(k-1) is old value of e @ t = (k-1)T, ... ;

Chapter 10 ME 440 9

Control Algorithm (Cont’d)Control Algorithm (Cont d)

1 Read *(k) from the interpolator1. Read x (k) from the interpolator.2. Read the position measurement x(k).p ( )3. Calculate the error: e(k) = x*(k) - x(k).4 C t th ti i l4. Compute the correction signal:

m(k)= -a1m(k-1) – a2m(k-2) - ... + b0e(k) + b1e(k-1) +...

5. Send m(k) to the output interface.6 Wait till the end of the period T6. Wait till the end of the period T.7. Go to Step 1.Chapter 10 ME 440 10

Control Algorithm (Cont’d)Control Algorithm (Cont d)

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Chapter 10 ME 440 11

Interpolatorp

• Interpolator is an advanced command generationInterpolator is an advanced command generation algorithm executed by the CNC system.

• By interpreting the codes in the default NC program, the i t l t t th f ll i dinterpolator generates the following commands:– The desired position and velocity of each axis– The desired velocity of spindle (and angular position whereverThe desired velocity of spindle (and angular position wherever

necessary) – The appropriate peripheral unit commands:

• Coolant on / off• Coolant on / off• Spindle on / off• Tool change

Th d i t d ith th ( d) hi l– The commands associated with the (canned) machine cycles.


Interpolator (Cont’d)p ( )

• Since the commands are to be fed to the• Since the commands are to be fed to the axis-position control (a.k.a. servo) cycle at

h li i d T t i tieach sampling period T, certain time restrictions are imposed on the interpolation algorithm.

• Furthermore the interpolator has to carry• Furthermore, the interpolator has to carry out complicated trigonometric calculations i l d i th t l di tiinvolved in the tool radius compensation.


Interpolation Types

• Three types of interpolations areThree types of interpolations are commonly utilized in CNC technology:– Rectilinear / Linear– Rectilinear / Linear– Circular

Helical– Helical• More advanced interpolation types are

l d i d CNC hi t lalso used in modern CNC machine tools:– Parabolic– NURBS


Linear Interpolationp

y

Y G90 G1 Xxf Yyf Zzf Ff • Let us first calculate travel time between these points:yf

f

p

)60/()()()( 222

fzzyyxx

T sfsfsft

−+−+−=

ys

X

)( f

• Hence, number of commands to be generated

xs xfX

zZ

gthrough out this motion becomes

⎫⎧T

zs

zf

f ⎭⎬⎫

⎩⎨⎧=TTN tint

Here int {•} rounds its argument

xs xfX

Here, int { } rounds its argumentto the nearest integer while Tdenotes the sampling time.


p g

Linear Interpolation (Cont’d)p ( )• The interpolation equations take the following form:

ykykyxkxkx

Δ+−=

Δ+−=

)1()()1()(

**

**

zkzkz Δ+−= )1()( **

• In these equations, q ,• k = 1, 2, ..., N;• x*(0) = xs; y*(0) = ys; z*(0) = zs

• The constants can be expressed as

zzyyxxNzz

zNyy

yNxx

x sfsfsf −=Δ

−=Δ

−=Δ ;;


Circular Interpolationp

The positions at t kT can be(x' y' )Y'

G90 G17 G3 Xxf Yyf Rr FfY

The positions at t = kT can beexpressed as

(x f ,y f)

(x'(k+1),y'(k+1))(x'(k),y'(k))

Y

)sin()(')cos()('

θθ

Δ=Δ=krkykrkxr

f

(x's ,y's)k

The positions at t = (k+1)Tbecome

f sX'O’(xc ,yc)

))1cos(()1(' θΔ+=+ krkxX

222

222 )()( ryyxx cscs =−+−

))1sin(()1(' θΔ+=+ krky222 )()( ryyxx cfcf =−+−

Solving these equations givesthe coordinates of the center (x y )


the coordinates of the center (xc,yc).

Circular Interpolation (Cont’d)

)(

Expanding these terms yields

)i ()()()i ()1(')sin()sin()cos()cos()1('

)'()'(

θθθθθθθθ

ΔΔΔΔΔΔ−ΔΔ=+

4847648476 kykx

kkkkrkrkx

)sin()cos()cos()sin()1(')'()'(

θθθθ ΔΔ+ΔΔ=+ 4342143421kxky

krkrky

When these equations are shifted backward in time(k←k-1), we get

)1(')sin()1(')cos()(')1(')sin()1(')cos()('

−Δ+−Δ=−Δ−−Δ=

kxkykykykxkx

θθθθ

with x’(0) = xs – xc and y′(0) = ys – yc.


Circular Interpolation (Cont’d)p ( )Note that

Nsf θθ

θ−

=Δ⎭⎬⎫

⎩⎨⎧ −

= ⋅

)(int Tfsfr

Nθθ

N ⎭⎩ 60

⎟⎞

⎜⎛ −⎟

⎞⎜⎛ − −− xxxx cscf 11 θθ ⎟

⎠⎞

⎜⎝⎛=⎟⎟

⎠⎜⎜⎝

= −−

rrcs

scf

f11 coscos θθ

Thus, we have

**cc ykykyxkxkx +=+= )(')(;)(')( **


ExamplepY [mm] G90 (ABSOLUTE COORDINATES)

G01 X0 Y0 Z0 F600 (PT 0)50

Samples to be generated

CD

G01 X0 Y0 Z0 F600 (PT 0)X20 Y10 (PT A)X60 (PT B)

v = 600[mm/min]

Y50 (PT C)X20 (PT D)Y10 (PT A)

10A B

X0 Y0 Z0 (GO TO PT 0)M30

X[mm]0 20 60

G90: Absolute Coordinates SpecifiedG01: Linear Interpolation Mode

X, Y, Z: Destination CoordinatesF: Feedrate (velocity in mm/min)


ME 440 - 09 CNC System (Rev. 3)

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Transcript of ME 440 - 09 CNC System (Rev. 3)